Is there a way to tell blender which images do not differ within an animation to render them just once?
This is not a straightforward process, but there is a recently released addon to do just this. The auther describes the details and provides a download on the link. 
The gist of it is that it renders a tiny version of each frame and compares it with the others to determine duplicates before rendering full size versions.

http://creativityhacker.ca/2017/08/08/dopplerender-a-turbo-boost-for-blender-animation-rendering/